### Video Transcript

Sarah is filling bags with
rice. The capacity of each bag is
two-thirds of a cubic decimeter. The mass of rice is 1.45 kilograms
per cubic decimeter. Work out the total mass of 30 bags
filled with rice. The mass of the bags can be
neglected.

Now, try not to worry too much
about the terminology here. A cubic decimeter is a measure of
volume. 1000 cubic decimeters are equal to
one cubic meter. However, we are given the mass per
single cubic decimeter. So we just need to deal with
these.

Let’s begin by working out the mass
of a single bag of rice. We’re told that the mass is 1.45
kilograms per cubic decimeter. We can write this as a ratio. For every 1.45 kilograms of rice,
its volume is one cubic decimeter. The capacity of each bag though is
only two-thirds of a cubic decimeter. To scale the right-hand side of our
ratio to two-thirds, we can simply multiply it by two-thirds since one multiplied by
two-thirds is two-thirds. Since this is a ratio, we must also
do this to the left-hand side.

The mass of a single bag of rice is
given by two-thirds multiplied by 1.45 kilograms. This isn’t a particularly nice
calculation to complete in our heads. So we’ll leave it in this form for
now. To find the mass of 30 bags of
rice, we’ll need to multiply this value by 30. That’s 30 multiplied by two-thirds
multiplied by 1.45.

Since multiplication is
commutative, that means it can be completed in any order. We can start by multiplying 30 by
two-thirds. If we write 30 as 30 over one, we
can cross cancel by dividing both 30 and three by three. That gives us 10 over one
multiplied by two over one. 10 multiplied by two is 20 and one
multiplied by one is one. 20 over one is simply 20.

We need to calculate then 20
multiplied by 1.45. 20 is the same as two times 10. So we’ll start by multiplying 1.45
by two. We could do this in our head or use
a formal written method. Let’s start by looking at the
column method.

Five multiplied by two is 10. So we put a zero in this column and
carry the one. Four multiplied by two is
eight. And then, when we add that one, we
get nine. Since only one of the numbers is a
decimal, we can carry the decimal point directly below the one in our question. And then, one multiplied by two is
two. 1.45 multiplied by two is,
therefore, 2.9. Finally, we’ll multiply 2.9 by
10. When we multiply by 10, we move all
of the digits to the left one space. 2.9 multiplied by 10 is, therefore,
29.

The total mass of 30 bags filled
with rice is then 29 kilograms.